 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| A. V. Andreev, R. V. Goldstein, and Yu. V. Zhitnikov, "Calculation of the limit equilibrium of internal and boundary cracks with interacting surfaces in an elastic half-plane," Mech. Solids. 37 (4), 79-92 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
4 |
Pages |
79-92 |
| Title |
Calculation of the limit equilibrium of internal and boundary cracks with interacting surfaces in an elastic half-plane |
| Author(s) |
A. V. Andreev (Moscow)
R. V. Goldstein (Moscow)
Yu. V. Zhitnikov (Moscow) |
| Abstract |
Fracture processes often occur in situations with the
stress state in the crack region being equivalent to a field of compression and shear.
In such cases, fracture problems involve both the contact problem of
the mechanics of
deformable solids and the crack problem, and require special methods for
their solution, since the regions of contact are unknown.
It should be observed that contact between crack surfaces may be
caused not only by external loads but may also be due to specific features of
the crack shape [1-3], as well as interaction between cracks and
defects [4-5], and boundary of the elastic body [2].
For this reason, an investigation of the limit equilibrium of
boundary and near-surface cracks should take into account
possible interaction between crack surfaces.
We consider a two-dimensional problem for the stress-strain state of an elastic
half-plane weakened by an internal or a boundary crack
with curvilinear surfaces subject to friction. A method is developed for
the analysis of the limit equilibrium of such cracks in semi-infinite and
infinite domains. Our investigation of boundary cracks takes into account
specific properties of the solution near crack tips, and this requires
some asymptotic analysis. We obtain solutions for the problem of equilibrium
of an arbitrarily oriented rectilinear (internal or boundary) crack
with contact surfaces in an elastic half-plane and various
loading conditions.
Previously, a similar problem was considered for a crack in an elastic plane [3].
Boundary cracks in an elastic half-plane, with contact between the surfaces neglected,
were considered in [2, 6-8]. The problem of stability of a boundary
rectilinear crack in a cracked half-plane, with contact friction between
the surfaces neglected, was considered in [9]. Some types of zigzag cracks
were studied in [10]. A radial crack issuing from a circular hole in an
elastic plane, with contact interaction of the surfaces with friction, was
investigated in [5]. Quasistatic growth of an arbitrary curvilinear crack
in an elastic half-plane (with contact between the surfaces neglected) was
studied in [11]. In [12], a statement of the problem was proposed for the
description of quasistatic growth of an arbitrary boundary crack whose
surfaces are interacting with friction when the elastic half-plane is
subjected to cyclic loads. |
| References |
| 1. | R. V. Goldstein and L. N. Savova,
"On the determination of opening and stress intensity factors
for a curvilinear crack in an elastic half-plane,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 2, pp. 69-78, 1972. |
| 2. | M. P. Savruk, Two-Dimensional Elasticity Problems for Bodies with
Cracks [in Russian], Naukova Dumka, Kiev, 1981. |
| 3. | A. V. Andreev, R. V. Goldstein, and Yu. V. Zhitnikov,
"Equilibrium of curvilinear cracks with formation of regions of contact,
slip, and stick between the crack surfaces," Izv. AN. MTT [Mechanics of
Solids], No. 3, pp. 137-148, 2000. |
| 4. | R. V. Goldstein, Yu. V. Zhitnikov, and T. M. Morozova,
"Equilibrium of a system of cuts with regions of contact and opening,"
PMM [Applied Mathematics and Mechanics], Vol. 55, No. 4, pp. 672-678, 1991. |
| 5. | M. Comninou and F.-K. Chang,
"Effects of partial closure and friction on a radial crack emanating from
a circular hole," Intern. J. Fracture, Vol. 28, No. 1, pp. 29-36, 1985. |
| 6. | V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshin,
Stress Distribution near Cracks in Plates and Shells [in Russian],
Naukova Dumka, Kiev, 1976. |
| 7. | V. V. Panasyuk, Limit Equilibrium of Brittle Bodies with Cracks [in Russian],
Naukova Dumka, Kiev, 1966. |
| 8. | W. Zang and P. Gudmundson,
"An integral equation method for piece-wise smooth cracks
in an elastic half-plane,"
Fracture Mech., Vol. 32, No. 6, pp. 889-897, 1989. |
| 9. | V. Petrova, V. Tamuzs, and T. Mescheryakova,
"Fracture of a semi-infinite medium containing a macrocrack
and microcracks," in Proc. Fracture:
Mechanisms and Mechanics. Damage and Failure. 11th Biennial Europ.
Conf. on Fracture, Vol. 1, pp. 283-288, France, 1996. |
| 10. | W. Zang and P. Gudmundson, "Frictional contact of kinked cracks
modelled by a boundary integral method," Intern. J. Numer. Methods in Eng.,
Vol. 31, No. 3, pp. 427-446, 1991. |
| 11. | A. P. Datsyshin, G. P. Marchenko, and V. V. Panasyuk,
"On the theory of crack growth with rolling contact,"
Fiz. Khim. Mekh. Mater., No. 4, pp. 49-61, 1993. |
| 12. | O. P. Datsyshin and V. V. Panasyuk,
"Durability and fracture calculation model of solids under their
contact interaction," Proc. Fracture: Mechanisms and Mechanics.
Damage and Failure. 11th Biennial Europ.
Conf. on Fracture, Vol. 2, pp. 1381-1385, France, 1996. |
| 13. | N. I. Muskhelishvili,
Some Basic Problems in Mathematical Elasticity [in Russian], Nauka, Moscow, 1966. |
| 14. | N. I. Muskhelishvili,
Singular Integral Equations [in Russian], Nauka, Moscow, 1968. |
| 15. | A. M. Lin'kov,
A Complex Method of Boundary Integral Equations in Elasticity [in Russian],
Nauka, St. Petersburg, 1999. |
| 16. | M. M. Chawla and T. R. Ramacrishnan,
"Modified Gauss-Jacobi quadrature formulas for the numerical evaluation of
Cauchy type singular integrals," BIT, Vol. 14, No. 1, pp. 14-21, 1974. |
| 17. | F. E. Erdogan, G. D. Gupta, and T. S. Cook,
"The numerical solution of singular integral equations,"
in Mechanics of Fracture, Vol. 1, pp. 368-425, Noordhoff Intern.
Publ., Leyden, 1974. |
| 18. | A. V. Andreev, R. V. Goldstein, and Yu. V. Zhitnikov,
Calculation of Limit Equilibrium of Internal and Boundary Cracks
with Interacting Surfaces. Preprint No. 692 [in Russian], Institute for
Problems in Mechanics, Moscow, 2001. |
| 19. | M. L. Williams, "Stress singularities from various boundary
conditions in angular corners of plates in extension," J. Appl. Mech.,
Vol. 19, No. 4, pp. 526-528, 1952. |
| 20. | R. V. Goldstein and Yu. V. Zhitnikov,
"Analysis of slip of crack surfaces with
friction forces under complex loading," Izv. AN SSSR.
MTT [Mechanics of Solids], No. 1, pp. 139-148, 1991. |
| 21. | P. S. Theocaris and N. J. Ioakimidis,
"The V-notched elastic half-plane problem,"
Acta Mech., Vol. 32, No. 1-3, pp. 125-140, 1979. |
| 22. | B. Paul,
"Macroscopic criteria for plastic flow and brittle fracture," in
H. Liebowitz (Editor), Fracture. Volume 2, pp. 313-496, Academic Press,
New York, 1968. |
| 23. | R. V. Goldstein and R. L. Salganik,
"Brittle fracture of bodies with arbitrary cracks,"
in Advances in Mechanics of Solids[in Russian], pp. 156-171, Nauka, Moscow, 1975. |
|
| Received |
08 April 2002 |
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